Technology for time travel cannot exist because the rules of nature as we understand them don't permit it. I don't think anybody would claim that physics rules out artificial intelligence in the same way.

No quite. Many theories support the ability to travel through time in one form or another, directly or as a byproduct of other processes. Regardless of what the true answer is, nature itself is not the governing body.

Our knowledge in general is still very immature. Because of that, our ability to comprehend vast and complex subjects like these is severely limited. Simply put, humanity is sucking its thumb and wearing diapers. And even that may be giving us too much credit.